Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 2x}{x + 6} = \dfrac{5x + 4}{x + 6}$
Answer: Multiply both sides by $x + 6$ $ \dfrac{x^2 + 2x}{x + 6} (x + 6) = \dfrac{5x + 4}{x + 6} (x + 6)$ $ x^2 + 2x = 5x + 4$ Subtract $5x + 4$ from both sides: $ x^2 + 2x - (5x + 4) = 5x + 4 - (5x + 4)$ $ x^2 + 2x - 5x - 4 = 0$ $ x^2 - 3x - 4 = 0$ Factor the expression: $ (x - 4)(x + 1) = 0$ Therefore $x = 4$ or $x = -1$